Is it possible to split electricity consumption of a heavy-duty-home-appliance - like a washing machine, for ex. - between two distinct apartments (splitting usage costs)? Something like this...
It can be done
How well you do it depends on the level of trust between the occupants.
Technically, it helps that you're in Europe and dealing with plain 1-leg single-phase power, so you only have to switch 2 wires and not 3 as in America. You need to switch all hots and neutral. You don't need to switch ground if both services rely on the same grounding rods/pipes/etc. for ground. Either ground will do.
Part 1: Controlling power.
The simplest way I can think of to assure a user only powers their own usage is a timer run-down switch. Each tenant sets some time on their switch, during which time the dryer is supplied from their system.
Part 2: Hard separation
It's not as simple as switching power. There absolutely must be no possibility, whatsoever, of both apartments feeding the same wire at the same time. That's because when an electrician services a house, he does not systematically inspect for really strange stuff. He works where he's paid to, and rightly assumes the house is wired normally. Because of this, abnormal is illegal. Not least, the power company might move apartment A to a different phase of the supply, meaning the hots from those two apartments oppose each other by 385 volts. Imagine if both turned on their switch at once!
The simplest way is to have each timer switch feed a different receptacle, and have the tenants move the washer/dryer from one receptacle to another. There are two problems with this approach. #1, it's tedious, and receptacles of that size are not made for daily changeover. #2, dryers take a lot of current, and good chance the timer switches aren't rated for that, so you need relays anyway. Since you need relays, you might as well use them for automatic changeover.
A changeover relay to guarantee separation
You can feed one receptacle with two supplies, but you need changeover relays to guarantee that.
A DPDT relay guarantees both sides can never be connected at once. This must switch both hot and neutral on the appliances. The "common" goes to the appliance(s). The Normally Closed side goes to tenant A's hot and neutral. Normally Open goes to tenant B's hot and neutral. (remember we're in Europe, in North America use a 3PDT relay.) What energizes the relay? The coil is connected to tenant B's timer switch.
Now, if your timer-switches are burly enough to switch the entire load of the washer and dryer, you're done. You are supplying that changeover relay from the timer, and when the timer runs down, power is cut.
Another relay to switch power
If the timer switches can't switch the full load of washer+dryer, you must hardwire both tenant's power through relays, and the timer circuit becomes a lightweight circuit that only operates relay coils. But we need another relay. Right now, the changeover relay feeds A's power at all times unless B throws his switch, so A's switch does nothing and B can wash at A's expense just by not throwing his switch. We can't have that.
So we have another relay to turn off A's side of the power unless A's switch is on. This is a plain, simple DPST relay as is commonly used in air conditioners, here in the States they cost about $12. Very straightforward. It goes upstream of the changeover switch, with its normally-open contacts to A's supply, and common to A's side of the changeover relay. Its coil is controlled by A's timer switch.
This means power from A goes through 2 relays, but power from B goes through only one. You could add a second relay for B, in similar fashion, but you still need the changeover relay!
If washer and dryer are fed by different circuits, then you need a second tranche of relays, one per circuit. Or different poles on 4-pole relays, but that wiring could get very confusing, particularly with neutrals. Neutrals matter; RCDs are why.
The cheapest way to do it is to estimate the power used per load, possibly using something like this: Kill-o-Watt electric usage monitor, but appropriate for your local power. Then keep a log of who uses it. This assumes a certain amount of trust of course, and you are dealing with in-laws, so good luck with that.
A changeover relay would work...
Harper's suggestion of a changeover relay, or Ratchet Freak's submetering suggestion, are both serviceable ones for a small-scale situation like this, and worth exploring if you can't have any changes made to the building's utility service. Keep in mind that some electrical codes (including the NEC in 210.25) prohibit this, although local inspectors probably aren't going to take this too seriously if the utility refuses to help you here by providing a separate service for the common area and you can provide them with documentation showing so.
However, you aren't the only person with this problem
Apartments and condominiums the world over have electrical circuits feeding shared (vs tenant) spaces, for a variety of reasons: lighting, receptacles, building core facilities such as elevators and whatnot, fire protection, and your case of a shared laundry facility.
Instead of using one or more tenant circuits and basically reimbursing or splitting the cost among the tenants involved, though, they use a separate service from the utility for the common area, with its own utility meter and service panelboard. That way, the landlord or condominium association gets a bill for the common area usage, independent of the individual tenant or member electrical bills.
This is spelled out for the USA in 210.25 of the NEC (your electrical regulations may specify something similar):
210.25 Branch Circuits in Buildings with More Than One Occupancy.
(A) Dwelling Unit Branch Circuits. Branch circuits in each dwelling unit shall supply only loads within that dwelling unit or loads associated only with that dwelling unit.
(B) Common Area Branch Circuits. Branch circuits installed for the purpose of lighting, central alarm, signal, communications, or other purposes for public or common areas of a two-family dwelling, a multifamily dwelling, or a multi- occupancy building shall not be supplied from equipment that supplies an individual dwelling unit or tenant space.